The invention concerns the problem of frequency synchronization within an airborne context, notably exhibiting low signal-to-noise ratios and Doppler accelerations that can reach values that are considered high in the field. The Doppler effect is caused by the movement of the aeroplane in relation to the satellite, and the aeronautical channel is perturbed by the frequency shift in the received carrier, called the Doppler effect.
FIG. 1 schematically shows a transmission system having a ground station, 1, a satellite 2 and an airborne system 3 or aeroplane. The outbound path La is defined as the one that goes from the ground station 1 to the airborne system, such as an aeroplane; the return path Lr is defined as the path that goes from the aeroplane 3 to the ground station 1, via the satellite 2. The Doppler effect is caused by the movement of the aeroplane 3 in relation to the satellite 2. It is possible to link the Doppler effect and the Doppler effect variation to the speed and acceleration of the aeroplane.
Let fem be the frequency of the transmitting system and vem be the speed thereof, frec be the frequency of the receiver and vrec be the speed thereof. The relationship between the two frequencies can then be expressed as a function of the speed c of light:
      f    rec    =                    c        -                  v          rec                            c        -                  v          em                      ⁢          f      em      
The satellite being able to be considered to be immobile vis-à-vis the aeroplane, the following is obtained for the frequency difference Δf between the transmitter and the receiver:
            f      em        -          f      rec        =            Δ      ⁢                          ⁢      f        =                            v          rec                c            ⁢              f        em            
It is then possible to link Dmax, the maximum Doppler effect, and Vmax, the maximum variation in the Doppler effect, to Smax, the maximum speed of the aeroplane, and Amax, the maximum acceleration of the aeroplane, in the following manner:
            D      max        =                            s          max                c            ⁢              f        em            ⁢                          ⁢      expressed      ⁢                                        ⁢                                      ⁢      in      ⁢                          ⁢      Hz                  v      max        =                            f          em                c            ⁢              A        max            ⁢                          ⁢      expressed      ⁢                          ⁢      in      ⁢                          ⁢      Hz      ⁢              /            ⁢      s                      The <<worst case>> aeronautical conditions that are considered here are as follows:                    a maximum speed of the aeroplane of 0.97 Mach, corresponding to the cruise speed of an airliner,            a maximum acceleration of the aeroplane of 2 g, corresponding to the maximum acceleration that can be reached by an airliner during:                            take off and landing oriented in the direction of the satellite,                a tight turn with the radial acceleration oriented in the direction of the satellite,                an air pocket with the satellite at the zenith in relation to the aeroplane.                The two graphs in FIGS. 2A and 2B show the acceleration A and the variation in altitude Alt in the presence of an air pocket, and the Doppler effect D and the variation in Doppler effect, induced curve V, respectively.The radio-frequency RF transmission characteristics are as follows:                                                a maximum carrier frequency fixed at 30 GHz, typical of the Ka band, the highest frequency range used in telecommunication satellites,        a minimum symbol rate, fixed at 1 Mbaud, corresponding to the minimum symbol rates used in satellite communications in the Ka band.        
The following values are determined for the maximum Doppler effect Dmax and the maximum variation in the Doppler effect Vmax:Dmax=33 kHz and Vmax=1962 Hz/s.By normalising these values in relation to the symbol rate Rs of the frame, the normalised maximum Doppler Dmaxnorm and the normalised Doppler variation Vmaxnorm are obtained:
  {                                                                                                              D                    max                    norm                                    =                                                            D                      max                                                              R                      S                                                                                                                                                                V                    max                    norm                                    =                                                            V                      max                                                              R                      S                      2                                                                                                    ⁢                                          ⁢                      D            max            norm                          =                              0.033            ⁢                                                  ⁢                          symb                              -                1                                      ⁢                                                  ⁢            and            ⁢                                                  ⁢                          V              max              norm                                =                      1.962            *                          10                              -                9                                      ⁢                          symbs                              -                2                                      ⁢                                                  ⁢                          R              s                        ⁢                          :                        ⁢                                                  ⁢            symbols            ⁢                          /                        ⁢            s                              ;                        V          max                ⁢                  :                ⁢                                  ⁢                  (                      Hz            ·                          s                              -                1                                              )                    ;                        D          max          norm                ⁢                  :                ⁢                                  ⁢                  symbs                      -            1                                ,                  ⁢                  V        max        norm            ⁢              :            ⁢                          ⁢                        symbs                      -            2                          .            
FIG. 3 shows the structure of a DVB-S2 frame made up of a header of 90 symbols, 300, of a first block 3011 of 1440 data symbols followed by a first block 3021 of pilots of 36 symbols, then a second block 3012 of 1440 data symbols followed by a second block 3022 of pilots of 36 symbols, and so on.
Within the aeronautical context, in the Ka band, the standardised structure of DVB-S2 frames that is associated with the frequency synchronisation mechanisms recommended in the ETSI directives TR 102 376 V1.1.1, “Technical Report, DVB, User Guidelines for the second generation system for Broadcasting, Interactive Services, News Gathering and other Broadband Satellite Applications DVB-S2”, does not allow operation for low symbol rates, lower than 5 Mbaud, for a signal-to-noise ratio lower than 5 dB, a value typical of the field.
In this instance of application, the maximum residual Doppler after Doppler estimation must bring about a maximum phase shift of π between two pilot blocks in order to prevent phase ambiguities. This involves a maximum frequency resolution ΔfMax equal to:
      Δ    f    Max    =                    π                  2          *          π          *                      (                          1440              +              36                        )                              *              R        s              =                            1                      2            *            1476                          *                  R          s                    =              3.38        *                  10                      -            4                          *                  R          s                    
with 1440 data symbols, 36 pilot symbols for the DVB-S2 frame.
FIG. 4 schematically shows an example of frequency estimation according to the prior art at a receiver. The frequency synchronisation of the signal takes place in two steps, a first rough synchronisation being effected by a looped structure I and a second, finer synchronisation being effected in open-loop or “feed-forward” control mode, II. The input signal received by the receiver enters a mixer 400 that also receives the estimated frequency value allowing a correction of the frequency when the device is operating. The signal is passed through an outfit comprising a Nyquist filter block, 410, a rate synchronisation module 420, a frame synchronisation module 430 and a first frequency synchronisation module 440, the output of which is connected firstly to a fine synchronisation module 406 followed by a phase acquisition module 470 and secondly to a loop filter 460.
The loop synchronisation scheme I comprises the frequency synchronisation module 440 and the module 450 of the loop filter. The frequency synchronisation module performs an estimation of the frequency of the signal {tilde over (f)} according to the formula:{acute over (f)}=arg(zkz*k-2)where zk=rka*k, where rk is the data sample r received at the instant k, a*k is the conjugate of the reference symbol at this same instant k and arg is the argument from a complex number. This estimation, which is very sensitive to noise, is then filtered by the first-order loop filter, and then injected as an input correction for the Nyquist reception filter.
The loop bandwidth of the loop filter is a determining parameter in the process of first frequency synchronisation:                it is proportional to the speed of convergence of the synchronisation,        it is likewise proportional to the sensitivity of the estimation to noise.        
In summary, the wider the loop band, the more rapidly it converges on the shift in frequency, but at the same time it is more sensitive to the noise level.
The next, fine synchronisation block 440 effects a second estimation of the frequency of the signal by using an algorithm operating in supervised mode: it uses the reference fields of the DVB-S2 frame (header and pilots) in order to effect its estimation.
For the record, it is possible to estimate the autocorrelation R(m) of a signal x for an index m by means of Rl(m) over a sequence of magnitude N:
            R      l        ⁡          (      m      )        =            1              N        -        m              ⁢                  ∑                  k          =                      m            +            1                          N            ⁢                        x          ⁡                      (            k            )                          ⁢                              x            *                    ⁡                      (                          k              -              m                        )                              The supervised algorithm from the Luise & Reggianini algorithm known to a person skilled in the art averages these correlations over a number L of pilot blocks. The correlations are effected over half of the length of a pilot block
      N    =                  L        0            2        ,where L0 is the length of a pilot block:
            f      ~        =                  1                  π          ⁢                                          ⁢                                    T              s                        ⁡                          (                              N                +                1                            )                                          ⁢              arg        ⁡                  (                                    ∑                              l                =                1                            L                        ⁢                                          ∑                                  m                  =                  1                                N                            ⁢                                                R                  l                                ⁡                                  (                  m                  )                                                              )                      ,  whereTs symbol timeL0: length of a pilot blocki: index of the estimate of the autocorrelationN: L0/2: number of autocorrelations produced by a pilot blockI: index of the pilot blockL: number of pilot blocks on which the frequency estimate is produced.This frequency correction gives rise to a second compromise concerning the value of the number L of pilot blocks over which to average the correlations: it is proportional to the precision of the estimate, and is inversely proportional to its reactivity.
However, such a scheme does not allow an adjustment for the frequency synchronisation to be found that allows notably the frequency variations of the aeronautical channel to be followed, and a sufficiently precise frequency estimation to be provided, even with a low signal-to-noise ratio, 0 dB. The frequency differences between the estimated frequency {tilde over (f)} and the real frequency freel can appear and be at the origin of dropouts and hence frame losses during communication.
The known estimators of the prior art are generally based on supervised algorithms using known information, such as the header and the pilot blocks of the DVB-S2 frame, which does not allow the conjugate of an estimate of the Doppler that is sufficiently precise to operate according to the DVB-S2 standard and sufficient reactivity in order to withstand the substantial Doppler variations owing to the movement of the aeroplane.
The document by RYU et al. entitled “Hardware efficient frequency estimator based on data-aided algorithm for digital video broadcasting system” describes a looped DA estimator that is averaged over time.
The document US 2008/0211719 describes an algorithm for estimating the blind frequency using the pilots.